Gravity from the extension of spatial diffeomorphisms

Abstract

The possibility of the extension of spatial diffeomorphisms to a larger family of symmetries in a class of classical field theories is studied. The generator of the additional local symmetry contains a quadratic kinetic term and a potential term which can be a general (not necessarily local) functional of the metric. From the perspective of the foundation of Einstein's gravity our results are positive: The extended constraint algebra is either that of Einstein's gravity, or ultralocal gravity. If our goal is a simple modification of Einstein's gravity that for example makes it perturbatively renormalizable, as has recently been suggested, then our results show that there is no such theory within this class.

34 pages

References in corpus (6)

• Quantum Gravity at a Lifshitz Point
• A Trouble with Hořava-Lifshitz Gravity
• A dynamical inconsistency of Horava gravity
• On IR solutions in Horava gravity theories
• Is nonrelativistic gravity possible?
• The Campbell--Magaard Theorem is inadequate and inappropriate as a protective theorem for relativistic field equations

Cited by in corpus (12)

• General Covariance in Quantum Gravity at a Lifshitz Point
• General Covariance in Gravity at a Lifshitz Point
• A functional renormalization group equation for foliated spacetimes
• Cauchy Slice Holography: A New AdS/CFT Dictionary
• Renormalization group flow of Hořava-Lifshitz gravity at low energies
• Finite Cutoff AdS${}_5$ Holography and the Generalized Gradient Flow
• On the Origin of Gravitational Lorentz Covariance
• Hamiltonian analysis of non-projectable modified F(R) Hořava-Lifshitz gravity
• General Covariance from the Quantum Renormalization Group
• Extending the rigidity of general relativity
• Extended Hořava Gravity with Physical Ground-State Wavefunction
• How General Relativity and Lorentz Covariance Arise from the Spatially Covariant Effective Field Theory of the Transverse, Traceless Graviton